Displaying similar documents to “New results on stability of periodic solution for CNNs with proportional delays and D operator”

Stable periodic solutions in scalar periodic differential delay equations

Anatoli Ivanov, Sergiy Shelyag (2023)

Archivum Mathematicum

Similarity:

A class of nonlinear simple form differential delay equations with a T -periodic coefficient and a constant delay τ > 0 is considered. It is shown that for an arbitrary value of the period T > 4 τ - d 0 , for some d 0 > 0 , there is an equation in the class such that it possesses an asymptotically stable T -period solution. The periodic solutions are constructed explicitly for the piecewise constant nonlinearities and the periodic coefficients involved, by reduction of the problem to one-dimensional maps. The...

Stability of unique pseudo almost periodic solutions with measure

Boulbaba Ghanmi, Mohsen Miraoui (2020)

Applications of Mathematics

Similarity:

By means of the fixed-point methods and the properties of the μ -pseudo almost periodic functions, we prove the existence, uniqueness, and exponential stability of the μ -pseudo almost periodic solutions for some models of recurrent neural networks with mixed delays and time-varying coefficients, where μ is a positive measure. A numerical example is given to illustrate our main results.

Existence and uniqueness of periodic solutions for odd-order ordinary differential equations

Yongxiang Li, He Yang (2011)

Annales Polonici Mathematici

Similarity:

The paper deals with the existence and uniqueness of 2π-periodic solutions for the odd-order ordinary differential equation u ( 2 n + 1 ) = f ( t , u , u ' , . . . , u ( 2 n ) ) , where f : × 2 n + 1 is continuous and 2π-periodic with respect to t. Some new conditions on the nonlinearity f ( t , x , x , . . . , x 2 n ) to guarantee the existence and uniqueness are presented. These conditions extend and improve the ones presented by Cong [Appl. Math. Lett. 17 (2004), 727-732].

Generalized c -almost periodic type functions in n

M. Kostić (2021)

Archivum Mathematicum

Similarity:

In this paper, we analyze multi-dimensional quasi-asymptotically c -almost periodic functions and their Stepanov generalizations as well as multi-dimensional Weyl c -almost periodic type functions. We also analyze several important subclasses of the class of multi-dimensional quasi-asymptotically c -almost periodic functions and reconsider the notion of semi- c -periodicity in the multi-dimensional setting, working in the general framework of Lebesgue spaces with variable exponent. We provide...

Periodic solutions to a non-linear differential equation of the order 2 n + 1

Monika Kubicova (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

A criterion for the existance of periodic solutions of an ordinary differential equation of order k proved by J. Andres and J. Vorâcek for k = 3 is extended to an arbitrary odd k.

Three periodic solutions for a class of higher-dimensional functional differential equations with impulses

Yongkun Li, Changzhao Li, Juan Zhang (2010)

Annales Polonici Mathematici

Similarity:

By using the well-known Leggett–Williams multiple fixed point theorem for cones, some new criteria are established for the existence of three positive periodic solutions for a class of n-dimensional functional differential equations with impulses of the form ⎧y’(t) = A(t)y(t) + g(t,yt), t t j , j ∈ ℤ, ⎨ ⎩ y ( t j ) = y ( t ¯ j ) + I j ( y ( t j ) ) , where A ( t ) = ( a i j ( t ) ) n × n is a nonsingular matrix with continuous real-valued entries.

Positive periodic solutions of a neutral functional differential equation with multiple delays

Yongxiang Li, Ailan Liu (2018)

Mathematica Bohemica

Similarity:

This paper deals with the existence of positive ω -periodic solutions for the neutral functional differential equation with multiple delays ( u ( t ) - c u ( t - δ ) ) ' + a ( t ) u ( t ) = f ( t , u ( t - τ 1 ) , , u ( t - τ n ) ) . The essential inequality conditions on the existence of positive periodic solutions are obtained. These inequality conditions concern with the relations of c and the coefficient function a ( t ) , and the nonlinearity f ( t , x 1 , , x n ) . Our discussion is based on the perturbation method of positive operator and fixed point index theory in cones.

Existence of nonnegative periodic solutions in neutral integro-differential equations with functional delay

Imene Soulahia, Abdelouaheb Ardjouni, Ahcene Djoudi (2015)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

The fixed point theorem of Krasnoselskii and the concept of large contractions are employed to show the existence of a periodic solution of a nonlinear integro-differential equation with variable delay x ' ( t ) = - t - τ ( t ) t a ( t , s ) g ( x ( s ) ) d s + d d t Q ( t , x ( t - τ ( t ) ) ) + G ( t , x ( t ) , x ( t - τ ( t ) ) ) . We transform this equation and then invert it to obtain a sum of two mappings one of which is completely continuous and the other is a large contraction. We choose suitable conditions for τ , g , a , Q and G to show that this sum of mappings fits into the framework of a modification of...

Multiple positive solutions of a nonlinear fourth order periodic boundary value problem

Lingbin Kong, Daqing Jiang (1998)

Annales Polonici Mathematici

Similarity:

The fourth order periodic boundary value problem u ( 4 ) - m u + F ( t , u ) = 0 , 0 < t < 2π, with u ( i ) ( 0 ) = u ( i ) ( 2 π ) , i = 0,1,2,3, is studied by using the fixed point index of mappings in cones, where F is a nonnegative continuous function and 0 < m < 1. Under suitable conditions on F, it is proved that the problem has at least two positive solutions if m ∈ (0,M), where M is the smallest positive root of the equation tan mπ = -tanh mπ, which takes the value 0.7528094 with an error of ± 10 - 7 .

Remotely c -almost periodic type functions in n

Marco Kostić, Vipin Kumar (2022)

Archivum Mathematicum

Similarity:

In this paper, we relate the notions of remote almost periodicity and quasi-asymptotical almost periodicity; in actual fact, we observe that a remotely almost periodic function is nothing else but a bounded, uniformly continuous quasi-asymptotically almost periodic function. We introduce and analyze several new classes of remotely c -almost periodic functions in n , slowly oscillating functions in n , and further analyze the recently introduced class of quasi-asymptotically c -almost periodic...

Characterising weakly almost periodic functionals on the measure algebra

Matthew Daws (2011)

Studia Mathematica

Similarity:

Let G be a locally compact group, and consider the weakly almost periodic functionals on M(G), the measure algebra of G, denoted by WAP(M(G)). This is a C*-subalgebra of the commutative C*-algebra M(G)*, and so has character space, say K W A P . In this paper, we investigate properties of K W A P . We present a short proof that K W A P can naturally be turned into a semigroup whose product is separately continuous; at the Banach algebra level, this product is simply the natural one induced by the Arens...